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Journal Article

Matrix numerical method for probability densities of stochastic delay differential equations

Authors
/persons/resource/nils.antary

Antary,  Nils
Potsdam Institute for Climate Impact Research;

Holubec,  Viktor
External Organizations;

External Ressource

https://zenodo.org/records/10406336
(Supplementary material)

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Citation

Antary, N., Holubec, V. (2024): Matrix numerical method for probability densities of stochastic delay differential equations. - Journal of Physics A: Mathematical and Theoretical, 57, 23, 235001.
https://doi.org/10.1088/1751-8121/ad4752


Cite as: https://publications.pik-potsdam.de/pubman/item/item_30573
Abstract
Stochastic processes with time delay are invaluable for modeling in science and engineering when finite signal transmission and processing speeds can not be neglected. However, they can seldom be treated with sufficient precision analytically if the corresponding stochastic delay differential equations (SDDEs) are nonlinear. This work presents a numerical algorithm for calculating the probability densities of processes described by nonlinear SDDEs. The algorithm is based on Markovian embedding and solves the problem by basic matrix operations. We validate it for a broad class of parameters using exactly solvable linear SDDEs and a cubic SDDE. Besides, we show how to apply the algorithm to calculate transition rates and first passage times for a Brownian particle diffusing in a time-delayed cusp potential.